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We examine a four player stochastic game in which two of the players are representative
households and two of the agents are governments. The game is set in a two country
general equilibrium model where it is costly to transport goods between nations. At
the beginning of each period, each country receives a random endowment of a single
non-storable consumption good. Consumers determine optimal consumption levels and
goods shipments based on tax rates and the amount of endowments received that period.
Governments determine optimal tax rates and expenditure levels in a strategic form stage
game. With complete financial markets, the terms of trade are determined by the relative
amounts of goods remaining in each country after taxation and thus governments can
manipulate the pattern of trade through tax policies. The choice between cooperating
or acting independently in the stage game creates a Prisoners' Dilemma. In the short
run governments refuse to cooperate and resort to "beggar thy neighbour" tax policies;
each government attempts to better its own domestic situation by over-taxing in order
to prey on the resources of its opponent. In an application of the Folk Theorem we find
that the long run behaviour is cooperative and over-taxation is avoided, provided that
governments and households are sufficiently patient.
The addition of transportation costs adds another dimension to the short run behaviour
of governments. In the same model without transportation costs, governments
implement a single optimal policy strategy that is independent of the direction of net
flow of goods and a unique pure strategy Nash Equilibrium always exists for the stage
game. When transportation costs are introduced the optimal behaviour of households
partitions the endowment space into three separate shipping regions: a foreign export, domestic export and no shipping region. In this setting governments can set policy rules
contingent upon the current direction of trade, and are thus able discriminate against
unfavourable patterns of trade. The ability to manipulate particular directional flows of
goods combined with governments acting in their own self-interests results in the nonexistence
of a pure strategy Nash equilibrium in the stage game for certain distributions of
endowments. This outcome can be interpreted as a trade disagreement between the two
countries; a scenario where governments disagree as to which shipping state currently exists.
Repetition however can lead to cooperation. If the governments and households are
sufficiently patient, then, for the repeated game, there is a unique cooperative subgame
perfect equilibrium that prevents trade disputes from occurring.